Detecting a data set structure through the use of nonlinear projections search and optimization

Victor L. Brailovsky; Michael Har-Even

Kybernetika (1998)

  • Volume: 34, Issue: 4, page [375]-380
  • ISSN: 0023-5954

Abstract

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Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points (in the form of the corresponding projection) represents a good solution for the first or the second problem are presented. To find a good solution one uses a search and optimization procedure in the form of Evolutionary Programming. The problems of cluster validity and robustness of algorithms are considered. Examples of applications are discussed.

How to cite

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Brailovsky, Victor L., and Har-Even, Michael. "Detecting a data set structure through the use of nonlinear projections search and optimization." Kybernetika 34.4 (1998): [375]-380. <http://eudml.org/doc/33364>.

@article{Brailovsky1998,
abstract = {Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points (in the form of the corresponding projection) represents a good solution for the first or the second problem are presented. To find a good solution one uses a search and optimization procedure in the form of Evolutionary Programming. The problems of cluster validity and robustness of algorithms are considered. Examples of applications are discussed.},
author = {Brailovsky, Victor L., Har-Even, Michael},
journal = {Kybernetika},
keywords = {cluster structure; nonlinear projection; cluster structure; nonlinear projection},
language = {eng},
number = {4},
pages = {[375]-380},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Detecting a data set structure through the use of nonlinear projections search and optimization},
url = {http://eudml.org/doc/33364},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Brailovsky, Victor L.
AU - Har-Even, Michael
TI - Detecting a data set structure through the use of nonlinear projections search and optimization
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 4
SP - [375]
EP - 380
AB - Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points (in the form of the corresponding projection) represents a good solution for the first or the second problem are presented. To find a good solution one uses a search and optimization procedure in the form of Evolutionary Programming. The problems of cluster validity and robustness of algorithms are considered. Examples of applications are discussed.
LA - eng
KW - cluster structure; nonlinear projection; cluster structure; nonlinear projection
UR - http://eudml.org/doc/33364
ER -

References

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  1. Ballard D. H., Brown C. H., Computer Vision, Prentice–Hall, 1982 
  2. Brailovsky V. L., Har-even M., Detecting a data set structure through the use of nonlinear projections and stochastic optimization, In: Proc. 1st IARP TC1 Workshop on Statistical Techniques in Pattern Recognition, Prague 1997, pp. 7–12 (1997) 
  3. Everitt B. S., Cluster Analysis, Wiley, New York 1974 MR0455213
  4. Har–even M., Brailovsky V. L., 10.1016/0167-8655(95)00073-P, Pattern Recognition Lett. 16 (1995), 1189–1196 (1995) DOI10.1016/0167-8655(95)00073-P
  5. Jain A. K., Dubes R. C., Algorithms for Clustering Data, Prentice Hall, 1988 Zbl0665.62061MR0999135
  6. Jain A. K., Moreau J. V., 10.1016/0031-3203(87)90081-1, Pattern Recognition 20 (1987), 547–568 (1987) DOI10.1016/0031-3203(87)90081-1
  7. Porto V. W., Fogel D. B., Fogel L. J., 10.1109/64.393138, IEEE Expert 10 (1995), 3, 16–22 (1995) DOI10.1109/64.393138
  8. (ed.) S. C. Shapiro, Encyclopedia of Artificial Intelligence, Vol, 1, ‘Clustering’. Wiley, New York 1990, pp. 103–111 (1990) MR1059716
  9. Vapnik V. N., The Nature of Statistical Learning Theory, Springer Verlag, Berlin 1995 Zbl0934.62009MR1367965

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